49 
of floating Bodies, and the Stability of Ships. 
produced by altering these proportions, cannot be obtained 
except by mathematical investigation (a subject to be consi- 
dered in some of the following pages), yet a general idea of 
the causes by which so remarkable a difference is occasioned 
in the floating position of the two cylinders, will appear ob- 
vious by attending to the changes which take place in the 
position of the line of support, while the solid is inclined from 
the upright through a small angle. For whenever the line of 
support, in the direction of which the force of the fluid's pres- 
sure acts, does not pass through the centre of gravity of the 
floating body, that force must generate a motion of rotation 
round an horizontal axis which passes through the centre of 
gravity of the solid ; and must cause an elevation of those 
parts of the solid which are on the same side of the axis of 
motion with the line of support, and consequently must de- 
press those parts which are situated on the contrary side of 
that axis. Admitting, therefore, that the solid is adjusted 
with its centre of gravity and the centre of the immersed part 
precisely to the same vertical line, and that a small inclina- 
tion takes place round the axis of motion ; it will depend on 
the position of the line of support, whether that inclination 
shall be counteracted, so as to restore the solid to its upright 
position, or shall be augmented ; in which latter case the so- 
lid oversets. If the nature of the figure should be such as 
causes the line of support to be moved toward those parts 
which are immersed by the inclination, that inclination will 
be counteracted, because the pressure of the fluid generates 
angular motion in a direction contrary to that in which the 
solid is inclined ; but if the figure is such as causes the line of 
support to be moved toward those parts of the solid which 
mdccxcvi. H 
